lesbianism vs gayness

lesbianism and gayness both are nouns.

Word	Noun	Adjective	Verb	Adverb
lesbianism	Yes	No	No	No
gayness	Yes	No	No	No

As nouns, gayness is a hypernym of lesbianism; that is, gayness is a word with a broader meaning than lesbianism:

lesbianism: female homosexuality
gayness: a sexual attraction to (or sexual relations with) persons of the same sex

Other hypernyms of lesbianism include homoeroticism, homosexualism, homosexuality, queerness.

lesbianism (noun)	gayness (noun)
female homosexuality	a sexual attraction to (or sexual relations with) persons of the same sex